In a well-known paper, Roll (1978), discusses tests of the SML in a four-asset context:

a. Derive two effi cient portfolios in this four-asset model and draw a graph of the effi cient frontier.

b. Show that the following four portfolios are effi cient by proving that each is a convex combination of the two portfolios you derived in part a:

c. Suppose that the market portfolio is composed of equal proportions of each asset (i.e., the market portfolio has proportions [0.25, 0.25, 0.25, 0.25]). Calculate the resulting SML. Is the portfolio [0.25, 0.25, 0.25, 0.25] effi cient?

d. Repeat this exercise, but substitute one of the four portfolios from part b as the candidate for the market portfolio.

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Variance-covariance matrix Returns 0.10 0.02 0.04 0.05 0.06 0.02 0.20 0.04 0.01 0.07 0.04 0.04 0.40 0.10 0.08 0.05 0.01 0.10 0.60 0.09